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Planned Parenthood president: 'Listen to women'

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Conservatives want to defund Planned Parenthood

But they also need votes of moderates in the Senate to repeal Obamacare

(CNN)Conservative lawmakers who are already worried that the Republican Party isn't moving fast enough on Obamacare repeal are growing agitated about something else: that a provision to defund Planned Parenthood will get left out on the chopping block.

GOP Rep. Jim Jordan, a member of the conservative House Freedom Caucus, has publicly called on party leaders to take an immediate vote on a 2015 budget reconciliation bill that rolled back large chunks of the Affordable Care Act and stripped federal funding for Planned Parenthood (the bill was vetoed by then-President Barack Obama).

But that hasn't yet happened, and he's concerned that Planned Parenthood will continue to receive federal dollars.

"We're also hearing that the defund Planned Parenthood language may not stay in," Jordan told CNN in a recent interview.

That concern is echoed by others. One conservative GOP aide said the current understanding among some policy aides is that the Planned Parenthood provision "would be one of the first things to go" as lawmakers continue to hammer out the details of a repeal bill.

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This aide, who would only speak on background to share concerns that are being raised in private, said while conservative lawmakers feel strongly about defunding Planned Parenthood, repealing Obamacare is such an important political priority that taking out the Planned Parenthood provision would be unlikely to derail the repeal bill altogether.

Still, leaving out the Planned Parenthood piece is likely to draw fierce protest from conservative Republicans, who have long supported defunding the organization.

House Speaker Paul Ryan announced last month that Republicans will strip federal funding for Planned Parenthood as a part of the legislative process to roll back Obamacare.

That promise is particularly problematic in the Senate, where two pro-abortion rights senators, Susan Collins of Maine and Lisa Murkowski of Alaska, won't commit to approving the bill with the Planned Parenthood provision in it. Some moderate House Republicans are also likely to feel concerned that a bill that defunds Planned Parenthood could invite political pushback from constituents.

House Ways and Means Chairman Kevin Brady, who is leading the GOP effort to craft the reconciliation bill to repeal Obamacare, told reporters Monday that he strongly believes a provision to strip all taxpayer money for Planned Parenthood should be part of the legislation.

"I think it needs to be done -- absolutely," Brady said. "I think there is overwhelming consensus to do exactly that and I'm going to continue to push hard that it be included."